Gauge-reversing maps on cones, and Hilbert and Thompson isometries
英文摘要：
We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a collineation unless the Hilbert geometry is the projective space of a non-Lorentzian symmetric cone, in which case the collineation group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
